Abstract: Based on Taylor series expansion of the equations the third order analytical solutions of power system dynamical equations is derived by using normal form theory. In order to verify the theory proposed in this paper, numerical simulations are performed on a single machine infinite bus system and a four-generator two-area system. The linear, the second order, and the third order, solutions are compared, with two proximity indices defined in time domain and frequency domain, respectively. And Prony analysis is performed, testifying the existence of higher-order combination modes, which verifies the effectiveness of the third-order analytical solutions in the post-disturbance analysis of power system.